Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
572 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10589350 | C3 | direct (N × H) |
| 26. C3×#634 | C8 | semidirect |
| 74. #634 | C3×C8 | semidirect |
| 129. C33 | Q8⋊C8 | semidirect |
| 191. C32 | #4484 | semidirect |
| 192. C32 | C3×Q8⋊C8 | semidirect |
| 220. C3 | C3×#4484 | semidirect |
| 221. C3 | #10589350 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×#634 | 2 |
| C33×C4⋊C8 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| #10589350 | 3 |
| C3×#4484 | 3 |